temporal spaces and thematic development in … spaces and thematic development ... 3 see william e....

mark anson-cart wright

Temporal Spaces and Thematic Development in Beethoven’s Music1

Rhythm and form have been the focus of much recent theoretical work on music of the Classical period. Yet certain rhythmic features of thematic construction and development have not received the analytical attention they deserve. This article investigates one such feature, or process, that is especially characteristic of Beethoven’s music: the presentation and subsequent manipulation of foreground temporal spaces within themes or, more specifically, within basic ideas. Unlike many recent investigations into rhythm, the present study does not overtly draw upon Schenkerian theory and recent extensions of it. Nor does it systematically build upon recent theories of Classical form. Rather, it examines some striking examples of spaces on the surface of Beethoven’s themes, and attempts to make sense of the ways in which Beethoven plays with, or manipulates, those spaces. A brief survey of several examples of this phenomenon sets the stage for a more extended analysis of the Largo assai ed espressivo from the ‘Ghost’ Trio, Op. 70 No. 1.

In recent years, analytical research on the Classical period in general, and on Beethoven in particular, has grown most noticeably in two areas: rhythm and form. Two rhythmic studies dealing with ‘hypermetric conflicts’ and ‘irregularities at deep levels of reduction’, respectively, exemplify a general tendency among analysts to look beyond the rhythmic surface of Beethoven’s music.2 More recently, two major treatises on form in Classical music have reshaped the field of formal analysis; indeed, Formenlehre has undergone a remarkable renaissance.3 Notwithstanding the advances in these areas of research, certain rhythmic features of thematic construction and development in Classical music have yet to receive the analytical attention they deserve. This article investigates one such feature, or process, that is especially characteristic of Beethoven’s music: the presentation and subsequent manipulation of foreground temporal spaces within themes or, more specifically, within basic ideas. Unlike many recent investigations into rhythm, the present study does not overtly draw upon Schenkerian theory and recent extensions of it. Nor does it seek to extend, in a systematic way, recent theoretical accounts of Classical form. Rather, it examines some striking examples of spaces on the surface of Beethoven’s themes, and attempts to make sense of the ways in which Beethoven plays with, or manipulates, those spaces. While it does occasionally address rhythmic issues such as hypermetric conflicts, it does not, for

1 AnearlierversionofthisarticlewasreadattheDublinInternationalConferenceonMusicAnalysison23June

2005.

2 See Richard Cohn, ‘The Dramatization of Hypermetric Conflicts in the Scherzo of Beethoven’s Ninth

Symphony’,in:19th-Century Music15/3(1992),pp.188-206;FrankSamarotto,‘StrangeDimensions:Regularity

andIrregularityinDeepLevelsofRhythmicReduction’,in:CarlSchachterandHediSiegel(eds)Schenker

Studies 2,Cambridge:CambridgeUniversityPress,1999,pp.222-38.

3 SeeWilliamE.Caplin,Classical Form,NewYork:OxfordUniversityPress,1998;JamesHepokoskiandWarren

Darcy,Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata,New

York:OxfordUniversityPress,2006.AnumberoftheideasinthelatterstudyfirstappearedinHepokoski

andDarcy’sarticle,‘TheMedialCaesuraanditsRoleintheEighteenth-CenturySonataExposition’,in:Music

Theory Spectrum19/2(1997),pp.115-54,whichhadanimmediateimpactonthefield,thoughitappearedtoo

latetobecitedinCaplin’sbook.

114 dutch journal of music theory, volume 14, number 2 (2009)

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the most part, investigate relations or conflicts between time-spans on the foreground and divisions of time that may be inferred at deeper levels of structure.4

A broad survey of Beethoven’s instrumental music indicates that many of his basic ideas contain distinctive temporal spaces.5 While these spaces most often occur in opening or primary themes, they do not appear to be consistently associated with particular genres, forms, keys, or tempi. In this study, ‘space’ refers to a relatively large or conspicuous time-span within a basic idea – a time span filled, and perhaps also marked, by either silence or a single sustained sound. If the texture in which a basic idea is initially presented is unison or homorhythmic, then any space presented therein is easy to identify. If the texture consists of two or more distinct parts, it is still possible, though perhaps more challenging, to hear a relatively long rest or sustained note in one part – typically the main melody – as a space. In other words, a space can be perceived as such even if attacks occur in another part or parts during that time-span. In any case, I shall focus on spaces that are introduced in unison or homorhythmic textures. Subsequent manipulation of a space may occur either within the initial thematic statement, during what William Caplin calls the ‘continuation phrase’,6 or at later stages of the movement or piece, during complete or partial recurrences (or variations) of the same theme. When Beethoven presents a basic idea containing a space or spaces, he may give the impression of leaving room for subsequent thematic development; attentive and imaginative listeners may anticipate such development, even on a first hearing.7

A locus classicus of this process within a theme is the beginning of the Fifth Symphony (Example 1). The opening two gestures in bars 1-5 conclude with the sustained notes Eb and D, respectively. Each sustained note marks off a temporal space that is then ‘filled’ with new tonal content in the counterstatement that immediately follows. The powerful effect of this opening hinges on the contrast between the tonal, durational, and hypermetrical uncertainty of the opening two gestures, and the clarity of the four-bar groups (or hypermeasures) that follow. The relation between bars 1-5 and bars 6-14 is similar to that between a theme and a variation.8

This way of characterising Beethoven’s thematic process is not altogether new; Schoenberg called it ‘developing variation’. Yet my concept of space departs significantly from analytical work in the Schoenbergian tradition – especially the work of Caplin. Such approaches to thematic organisation or design in Classical music focus on entities such as the sentence, the period, and quatrain form, and describe development in terms of ‘liquidation’, ‘fragmentation’, and the like. The present study is meant to complement Caplin’s approach by drawing attention to the potential – be it manifest or latent – of Beethoven’s basic ideas for development.

4 See, for example,FrankSamarotto, ‘ATheoryofTemporalPlasticity inTonalMusic:AnExtensionof the

Schenkerian Approach to Rhythm with Special Reference to Beethoven’s Late Music’, PhD diss., City

UniversityofNewYork,1999.

5 Iusetheterm‘basicidea’asdefinedinCaplin,Classical Form,pp.37-39,whichdrawsheavilyonSchoenberg’s

theoryofthe‘sentence’(Satz).ThetermusedbySchoenbergis‘basicmotive’;seehisFundamentals of Musical

Composition,ed.GeraldStrangandLeonardStein,London:Faber&Faber,1967,p.21(where‘sentence’is

firstdefined).

6 Caplin,Classical Form,p.40.

7 Tobesure,suchmanipulationofspacesoccursinworksofotherClassicalcomposers,too.See,forexample,

Mozart’sStringQuintetinC,K.515,firstmovement.IhavechosentofocusonBeethovenlargelybecausehe

usesspacesmoreconspicuouslythanearliercomposersdo.

8 Caplin,inClassical Form,pp.35-36,analyzesbars6-21asasentence(seehisExample3.2).Inhisview,bars1-5

donotbelongtothesentencebut,rather,‘makeupathematicintroduction’(p.263,n.7).Butbars1-5present

anindispensableadumbrationofthebasicideasinbars6-14,andbars1-21maybeunderstood,accordingly,

asasinglethematicentity(orprocess).Inthisinstance,Caplinachievesformalconsistencyattheexpense

ofthematicprocess.

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A space, in the sense just described, is essentially a time-span. But it is often marked off, or filled, by tonal elements that are related spatially in the listener’s imagination. Thus, any consideration of space in this sense must also take pitch space of some kind into account. In the next section I set down a few theses concerning spaces, with a few illustrations from works of Beethoven. The third section presents an extended discussion of temporal spaces in the Largo movement of the ‘Ghost’ Trio, Op. 70 No. 1. I conclude with some remarks on the relation of temporal spaces to concepts of diminution.

Presentation and Manipulation of ‘Space’In order for a time-span between attacks to be heard as a space, it must be presented at least twice, in immediate or close succession, as in Example 1, bars 1-5. This requirement applies most readily, though not exclusively, to themes in the form of a sentence.9 Following the twofold presentation of the basic idea, there are two important ways in which the space therein may be varied or manipulated: (1) new material may be inserted into or superimposed on the space; or (2) previously presented material (itself subject to minor alteration) may be shifted onto or within the space. These two procedures can occur separately, successively, or simultaneously. Recognition of either procedure depends, of course, on preserving – to some degree – the original identity of the space being manipulated or varied. In Example 1, bars 6-14, the second violin line is nearly identical to the one in bars 1-5; this connection makes it possible to hear the entire passage as a sort of theme and variation (the G in bar 10 being a variant of the F in bar 3). The two variation procedures happen simultaneously. With respect to the sustained C in the cello and bassoon parts, we recognise the first procedure: the pitch C counts as newly ‘superimposed’ material that clarifies the space both tonally and harmonically. In the viola and first violin parts in bars 6-14, we may observe the second procedure, namely, the shifting of a previously presented motive onto the space, with slight intervallic adjustments. In these bars – brilliantly conceived as a quasi-canonic stretto – there is a perfect balance between the agitated rhythmic surface and the relatively slow pacing of tonic and dominant harmonies. (The harmonic rhythm accelerates, of course, after bar 14.)

9 Caplin,inClassical Form,p.39,describesthesentenceasbeginningwitha‘presentationphrase’consisting

ofastatementofabasicideaanditsimmediaterepetition,eitherexactorvariedinpitch.

Allegro con brio

stgs., cl.

8

vln.2cello,bsn.

vla.

vln. 1

spaces presented

spaces filled

Example 1Beethoven,SymphonyNo.5,firstmovement,bars1-15.

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It is not uncommon for the two variation procedures just described – superimposition of new material and shifting of previously stated material – to occur in succession, as in Example 2, bars 1-29 of the first movement of Beethoven’s String Quartet in F, Op. 18 No. 1. The principal motive or basic idea presented in bars 1-2 recurs many times in bars 1-20, always beginning on an odd-numbered bar; after bar 20, the motive’s placement is less restricted. The final attack of the motive, on the downbeat of bar 2, opens up a space that is subject to variation after the second (slightly varied) statement of the motive in bars 3-4. Following the presentation phrase in bars 1-4, the content of the even-numbered bars (or spaces) is varied in three stages, each more intense than the previous one:(1) In bar 6, a new melodic figure (marked by the bracket) appears, along with supporting

harmony; the silent spaces in bars 2 and 4 are thus ‘filled’ with sound in bar 6.(2) In bars 14 and 16, the spaces are filled in a more intense manner: melodically, by

means of dissonant appoggiaturas; and harmonically, by means of applied diminished seventh chords.

(3) In bars 22, 24, and 26, the lowest three parts exhibit not only the first procedure of superimposing material on the space (they are similar to bars 14 and 16 with respect to the type of harmony and figuration), but also the second procedure of shifting the principal motive onto the space – a motive that, until this point, has only occurred in odd-numbered (i.e., ‘strong’) bars.10

In a recent article on discontinuity in Beethoven’s Opus 18 quartets, Barbara Barry builds upon Theodor Adorno’s ideas of ‘intensive’ and ‘extensive’ time. In her words, ‘[i]ntensive time is characterised by taut motivic work, strategic use of silence, and juxtaposed changes of register and dynamics’ (as in the Quartetto Serioso, Op. 95).11 By contrast, ‘extensive’ time involves ‘greater continuity of line and phrase’ and ‘less angular rhythmic momentum’ (as in the ‘Harp’ Quartet, Op. 74).12 Barry characterises the first movement of Op. 18 No. 1 as ‘a playful version of intensive time’, and notes that the opening turn figure ‘is intensified through interlocking parameters – registral disjunction, harmonic dissonance, and sforzandi dynamics, as seen in [bars 21-22]’.13 I find her interpretation to be compatible with my account of the role of spaces in bars 1-29. However, the techniques with which I am especially concerned – superimposition and shifting of motivic material – are not only to be found in ‘intensive’ works. For example, the first movement of the ‘Waldstein’ Sonata, Op. 53 (discussed below) exhibits precisely these techniques, yet also embodies ‘extensive’ time. Before examining further examples of spaces, and the different ways in which Beethoven works with them, let us consider the following assertion by Caplin concerning basic ideas in Classical music:

‘Themelodicendofabasicideaisoftenmarkedbysilence,whichsetsofftheideafromsubsequentmaterial.Asimilareffectiscreatedwhenthefinalnoteoftheideaisrelativelylongerthanthosethatprecedeandfollowit.’14

10 IagreewithWallaceBerry,whohearsbar1asmetricallystrong(unlikeRogerSessions,whointerpretsbar

2asstrong,andwithwhomBerryexplicitlydisagrees).SeeBerry,Structural Functions in Music,Englewood

Cliffs,NJ:Prentice-Hall,1976,p.329.

11 BarbaraBarry,‘InBeethoven’sClockShop:DiscontinuityintheOpus18Quartets’,in:Musical Quarterly88/2

(2005),p.321.

12 Barry,‘InBeethoven’sClockShop’,p.321.

13 Barry,‘InBeethoven’sClockShop’,p.327.

14 Caplin,Classical Form,p.37.Toillustratethispoint,Caplinreferstobars7-10ofBeethoven’sFifthSympony,

whichhecallsabasicidea.(SinceCaplinbelievesabasicideamustoccupytwo‘real’bars,thesefournotated

barsareregardedasequaltotwo‘real’bars.)

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In other words, a basic idea often ends with a space that is occupied either by silence or by a relatively long, sustained sound. As we have just seen, a space at ‘the melodic end of a basic idea’ can become a breeding ground, so to speak, for continuation or, more broadly speaking, for thematic development. Without the presentation of such a space, the very techniques that exemplify Caplin’s ‘continuation function’ (fragmentation, acceleration, and so on), as well as superimposition and shifting of material, could not, in most cases, take place. Caplin’s theory of Classical form is coherent and explanatory as far as it goes, but it does not sufficiently acknowledge the role of basic ideas in formal contexts other than the first appearance of the themes to which they belong. The technique of rhythmic shifting – similar to stretto in fugal writing – may coincide with thematic fragmentation or liquidation. These techniques are most often found in development sections. For example, in the first movement of the ‘Waldstein’ Sonata, the two motives presented successively in the right hand of bars 3-4 appear in abbreviated form in bars 96ff., such that the space between the motives is eliminated, and the rate of motivic alternation is increased by a factor of two (i.e., two motives per bar). While thematic fragmentation normally occurs in development sections, manipulation of spaces may take place already within the opening theme or theme group (as shown in

vln.1

cresc.

vln.1

vla., cello vla.

cello

Allegro con brio

vlns.

spaces presented

vln.1

vln.2

8

space filled

motive shifted onto the space

15

22

Example 2Beethoven,StringQuartetinF,Opus18No.1,firstmovement,bars1-29.

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Examples 1 and 2). Another example of this phenomenon is the finale of the Piano Sonata in D major, Op. 10 No. 3, a seven-part rondo. The playful rondo theme contains numerous rests that might be heard as spaces just waiting to be filled. The rests in bars 1 and 2 have a halting effect that they probably strike many listeners as odd or willful. In contrast to the tentative character of these bars, the music in bars 3-4 proceeds impatiently, only to halt again, somewhat teasingly, at the fermata. Bars 1-4 form the antecedent of a period (a rather unusual period, to be sure); the spaces in bars 1-2 are filled during the consequent, starting at bar 5. Unlike bars 1-2, which contain just two statements of the initial motive, separated by two and a half beats of silence, bars 5-6 contain three statements of the motive, separated only by quaver rests. As if in answer to the rhythmic crowding in bars 5-6, Beethoven inserts a new space in bar 7, immediately after a deceptive cadence. Further manipulation of the space in the basic idea occurs in the second and third returns of the rondo theme (the first return being unaltered). In the second return, the space remains intact at first (bar 56), but is then filled with stretto imitations in the outer parts (bar 57). The stretto effect is intensified in bars 60-61. In the third return, the distinctive silence in the first bar of the theme has almost disappeared, since Beethoven has delayed the entry of the left hand’s triadic figure by half a bar. In other words, he has shifted the left-hand figure onto the space. In the next two bars, this figure appears decorated with passing semiquavers, and then fragmented into three-note segments. Viewed as a whole, the final statement of the theme differs most obviously from earlier ones with respect to the abundance of semiquavers – particularly in the penultimate bar, varied here for the first and only time. Beethoven thus exhausts the theme’s potential for variation qua rondo theme through acceleration of the figuration and increased motivic density (almost to the point of saturation), thereby drawing attention to the imminent closure of the movement and of the Sonata as a whole.15

Thus far, we have observed Beethoven’s treatment of spaces in the context of expositions and developments, and in one very striking example of a ‘variable’ rondo theme. It should also be noted that, at the beginnings of recapitulations, Beethoven not infrequently superimposes a new countermelody upon the primary theme, whether that theme contains a space in the strict sense or not. Three well-known examples – all from first movements – are the String Quartet in E minor, Op. 59 No. 2; the Piano Sonata in E major, Op. 14 No. 1; and the Piano Sonata in Bb (‘Hammerklavier’), Op. 106. Of these three, only Op. 59 No. 2 presents a space at the beginning – one of the most striking openings in the quartet literature – that is filled, and thus concealed, at the recapitulation (compare bars 1-2 and bars 141-42). One consequence of this procedure is that the border between the end of the development and the start of the recapitulation is somewhat obscured; the recapitulation seems to begin at bar 143 (= bar 3). This recasting of bars 1-2 – which could be heard at the start of the movement as either an introductory motto or an integral part of the primary theme – does not so much resolve as underscore the formal ambiguity of those bars. In any case, only at the end of the coda (bar 251) does the idea first presented in bars 3-4 acquire independence from the idea in bars 1-2 that, until then, always preceded it.

The Largo assai ed espressivo from the ‘Ghost’ Trio, Op. 70 No. 1In view of the great dramatic power of this movement, whose ‘ghostly’ effects inspired the Trio’s nickname, surprisingly little analytical work has been published on it.16 I shall

15 Interestingly,ateachreturnoftherondothemeonespaceremainsunaltered,liketheeyeofastorm:the

silenceintheseventhbar,immediatelyfollowingthedeceptivecadence.

16 SeeLewisLockwood,‘OntheProblemofClosure’,in:Beethoven: Studies in the Creative Process,Cambridge,MA:

HarvardUniversityPress,1992,pp.181-97;StefanKunze,‘Beethovens“Besonnenheit”unddasPoetische’,

in: Rudolf Bockholdt andPetraWeber-Bockholdt (eds)Beethovens Klaviertrios: Symposion München 1990,

Munich:Henle,1992,pp.145-67;LawrenceKramer,‘AnalysisWorldlyandUnworldly’,in:Musical Quarterly

87/1(2004),pp.119–39.

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focus on the history of the opening eight-bar theme, and particularly the treatment of the spaces in it each time it reappears. This theme, shown in Example 3a, establishes the key of D minor and presents two contrasting motives, labeled a and b, in steady alternation. The crotchets on the second beat of even-numbered bars open up spaces that will be filled later on, in a remarkable variety of ways. Here, unlike the examples discussed above, the spaces are not filled or manipulated right away, but rather gradually, and with increasing urgency as the piece unfolds.

The form of the movement is sonata without development. Example 3b reproduces most of the transition, which begins as a varied repetition of the opening theme. But it soon gravitates toward C major, the second key area – a rather unusual choice for a movement in D minor. With regard to the spaces, however, what is striking about the transition is not so much the modulation as the texture and, especially, the hypermetric design, as compared with bars 1-8. The pairing of cello and violin in bar 1 establishes a pattern for the first eight bars: odd-numbered bars tend to sound stronger than even-numbered ones, although the piano entrances create a kind of secondary emphasis on those bars. The transition further explores that tension or ambiguity in a number of ways. Thus, at the beginning of Example 3b, it is the cello and piano that are paired together, and they project bars 18 and

3 3cresc.

3

sotto voce

b3

bsotto voce

Largo assai ed espressivo

sotto voce

aspace (beat 2)

aspace (beat 2)

a a

b b

5

Example 3aBeethoven,TrioinDminor,Opus70No.1(‘Ghost’),secondmovement,bars1-8.

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20 as strong bars. The violin’s entrance in bar 19 provides the hypermetric foil originally embodied by the piano in bar 2. In bar 21, however, the piano asserts a new harmony, V7

of C major, which lends both harmonic and metric support to the violin. The piano has severed its ties with the cello, so to speak, and formed a new metric alliance with the violin. The cello part, unfazed by this, continues to project the initial pattern of two-bar groups; from the cellist’s point of view, arguably, bar 22 is strong.

3

3

12

21

12

21

cresc.

22

3

23

cresc. 3

24

3

25

cello +piano:

violin:

48

1 2

1

1

2

2cello only:violin +

piano: 1

leggiermente48

18 193

sotto voce

20 21

3

12

b (shifted)

Hypermeter:

26

Example 3b‘Ghost’Trio,secondmovement,bars18-26.

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And so, at this point, there is a conflict: bar 22 is strong for the cello but less strong for the piano and violin. I shall say more about the violin part presently. For now, let us consider the harmonies in the first four bars or so of Examples 3a and 3b. The first change of harmony occurs in bar 4 and at the equivalent point in the transition, bar 21; these harmonies are functionally equivalent. The continuation of the dominant in bar 22 makes bars 21-22 sound like a two-bar unit. That reading is confirmed by the ‘new’ event in the violin in bar 22: the appearance of motive b on beat two, rather than on the next downbeat. As the bracket in Example 3b above bar 22 indicates, b has been shifted back one beat so as to fill the original space that, in earlier bars, had been occupied by a single crotchet played on a different instrument. The shift of motive b creates a melodic drive toward the E on the downbeat of bar 23, which is supported by C-major 6

3 chord. There are two subsequent arrivals on C-major harmony, now in root position, in bars 27 and 31 (not shown in Example 3b), the latter being the definitive one. The emphasis on the downbeat of bar 23 helps clarify the metric identity of bars 21, 23 and 25 as strong bars (as compared to their weak counterparts in the opening theme, bars 4, 6 and 8). In bars 21-26, the violin and piano project the main hypermetre, which is supported by the changes of harmony. The cello alone projects a secondary hypermetre or ‘shadow metre’, to use Frank Samarotto’s term, which actually corresponds the main hypermetre of bars 1-8, asserted by the cello and violin.17

The opening theme – or, at least, the first two bars of it – appears five times in the course of the movement, always recognisable as a sort of re-beginning, but varied in one or more ways. Example 3 shows the five iterations of the theme’s beginning, to facilitate observation of differences between corresponding bars, with particular respect to events occurring on the second beat. These differences create a sort of narrative of the second beat in this movement. (We have already observed the first turning point in this narrative: the intrusion of motive b upon the second beat of bar 22.) Before considering other critical moments in this narrative, let us take another look at the beginning of the movement (Example 3a). Motive b in bar 2 is rhythmically active, yet tonally static, circling as it does around A. When the piano comes to rest on the crotchet A, attention is drawn not only to that pitch, but also to the temporal space following the attack. When motive b appears in bar 21 (see Example 3b), it circles around D; it is still tonally static. But, in bar 22, motive b is altered in two significant ways: it starts in the middle of the bar, and leads from D to E on the next downbeat. Motive b thus generates tonal motion to a new goal – something it had not done before.

17 SeeSamarotto,‘StrangeDimensions’,p.235.

3 3 3 3

3 3

sotto voce

46 48arcopizz.

Example 3c‘Ghost’Trio,secondmovement,bars46-49.

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At the start of the recapitulation (Example 3c), an altogether new melodic idea is presented in the piano: a syncopated repetition of the tonic, D, followed by a delicately ornamented ascending scale from D to A; the same idea appears two bars later, this time leading to Ab. Although the continuation is not shown, it may be noted that this new figuration also appears in bars 50 and 52. As one might expect, the recapitulated version of the transition intensifies the narrative considerably. This passage, shown in Example 3d, begins in D major; this is not just the parallel major, but also potentially the dominant of G (which, in turn, could be the dominant of C). That implication becomes stronger in bars 65 and 66, where F # diminished sevenths are sounded. The music after bar 66 follows a rather complicated path, which need not be described here; suffice it to say, D minor is eventually confirmed with the same material that had appeared in C major in the exposition. But, to return to our narrative: in bars 65 and 66, motive b is shifted back to the middle of the bar. What is striking here is that the shift happens two bars sooner than the one in m. 22. This early shift lends a sense of urgency to the recapitulation – an urgency that appropriately puts the spotlight on the ending of this movement, rather than on its middle.

The final chapter in the narrative of the second beat takes place in the coda. Only the first two bars of the coda are given in Example 3e, but the story is perfectly summed up in this small amount of time. First, there is the earliest possible intrusion of motive b: on the second beat of the first bar of the coda. Indeed, there are back-to-back statements of b by the violin and the piano. The latter statement leads to the climactic, yet anti-climactic, descending chromatic scale in the right hand of the piano: twenty different notes are heard within the second beat of the bar. Also within this beat the structural V-I cadence unfolds. From a rhythmic point of view, this is surely one of the oddest structural cadences in music of the Classic period.18

Temporal Spaces in Relation to Concepts of DiminutionThe notion of space presented here resonates with earlier concepts of diminution or elaboration. In the seventeenth and eighteenth centuries, the technique of varying or embellishing a simple melodic framework was demonstrated in such manuals as Christopher Simpson’s The Division-Violist (1659) and Friedrich Erhardt Niedt’s Musicalische Handleitung (1700). More than two centuries later, Heinrich Schenker

18 Thedescentofthefundamentalline(intheSchenkeriansense)occurshere,bar88,ratherthanatthevaried

repeatthatimmediatelyfollows(notshowninExample3e).

3

3 3

48

48

sotto voce

65b b

Example 3d‘Ghost’Trio,secondmovement,bars63-66.

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developed the concept of Auskomponierung (‘composing out’), which relates to Diminution (a term he used much less often), but embraces more levels of structure, and ultimately guarantees the synthesis or unity of the work.19 Whereas the manuals present performers and composers with the tools for creating spontaneous and/or planned variations upon melodic or harmonic frameworks, Schenker’s analyses reveal the relation between the underlying framework, or background, of existing compositions and their ‘composed-out’ middlegrounds and foregrounds. In the early 1970s, Leonard B. Meyer developed the concept of ‘gap-fill’ – the idea that, if a theme contains prominent melodic skips, the skips (or gaps) will be filled later in the theme or, perhaps, later in the piece.20 The emphasis in Meyer’s concept, as in Schenker’s concept of composing-out, is on pitch spaces. Whereas these theorists, like Niedt and others, are mainly concerned with showing ways of filling tonal spaces with tonal content, I have focused on temporal gaps within themes as spaces – or places – where tonal events may or may not subsequently occur. The form that displays techniques of diminution most obviously is variation form. Yet, one is no more likely to find spaces, in the sense used here, in a variation theme by Beethoven than in the primary theme of one his sonata forms. A striking example that deserves mention, however, is the Variations and Fugue on an Original Theme (‘Eroica Variations’), Op. 35, which begins with the well-known Basso del Tema. The silent spaces in bars 9 and 11 of the Basso (assuming the introductory bar to be bar 0) are strategically placed after the first reprise; they are heard to precede the attacks of the dominant note in bars 10 and 12. During three intermediate stages leading up to the theme proper, Beethoven adds counterpoints to the Basso (a due, a tre, and a quattro). In other words, he superimposes material onto the space, much as he does in the opening of the Fifth Symphony (Example 1). But the fact that this material is superimposed onto the entire Basso – not just the spaces within the Basso – illustrates a general difference between the variation procedures examined above in the context of non-variation forms, and what

19 On the relation between Auskomponierung and Diminution in Schenker’s writings, seeWilliam Drabkin,

‘HeinrichSchenker’,in:The Cambridge History of Western Music Theory,ed.ThomasChristensen,Cambridge:

CambridgeUniversityPress,2002,pp.821-22.

20 LeonardB.Meyer, Explaining Music: Essays and Explorations,Berkeley:UniversityofCaliforniaPress,1973,pp.

145-57.

cresc.3 6 6

cresc.

cresc.3

48

24 24 12 12

Example 3e‘Ghost’Trio,secondmovement,bars87–88.

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one finds in variation forms. In the former context, variation occurs locally and, often, in a relatively ad hoc manner. In variation forms, by contrast, each variation – generally speaking – exhibits a consistent texture throughout; a particular procedure is applied globally to each variation. The sort of motivic shifting that Beethoven uses so effectively on a local level in Op. 10 No. 3 and the ‘Ghost’ Trio, for example, would not typically occur in a set of variations, except (perhaps) when applied to a whole variation. This article has drawn attention to Beethoven’s use of space in some of his basic ideas, and has focused on two principal means of manipulating those spaces: superimposition of new material and shifting of existing material. While such spaces can also be found in works of Haydn and Mozart, they appear to be more frequent and conspicuous in Beethoven’s music – hence the focus of this article. The relation between spaces and larger formal units resists generalisation and, partly for this reason, I have not devised a sophisticated theory to explain these phenomena. In the meantime, analysts of form in the music of Beethoven (and others) would do well to take a closer look at temporal spaces and their role in thematic processes.

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